document.write( "Question 689725: how do I found the exact answer of sec(-5 pi/8)? I tried to add or subtract 2pi so that it is a value on the chart but that does not work and I don't know what else to try. I think maybe a double angle therom or something? \n" ); document.write( "

Algebra.Com's Answer #426037 by lwsshak3(11628) $\"\"$ $\"About$

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how do I found the exact answer of sec(-5 pi/8)?
\n" ); document.write( "use identity for cos half-angle formula: cos (s/2)=ą√[(1+cos s)/2]
\n" ); document.write( "-sec(-5π/8)=-1/cos(-5π/8)
\n" ); document.write( "solve for cos(-5π/8), then take the negative reciprocal.
\n" ); document.write( "cos(-5π/8)=cos(-5π/4)/2)=-√[1+cos(-5π/4)/2]
\n" ); document.write( "cos(-5π/4)=cos π/4=-√2/2 in quadrant II where cos<0
\n" ); document.write( "-√[1+cos(-5π/4)/2]=-√[1-√2/2/2]=-√(2-√2)/2
\n" ); document.write( "-sec(-5π/8)=-1/cos(-5π/8)
\n" ); document.write( "-sec(-5π/8)=-1/-√(2-√2)/2
\n" ); document.write( "-sec(-5π/8)=2/√(2-√2)
\n" ); document.write( "check with computer:
\n" ); document.write( "cos(-5π/8)=-.3836
\n" ); document.write( "-sec(-5π/8)≈-1/-.3836=2.6131..
\n" ); document.write( "2/√(2-√2)≈2.6131..
\n" ); document.write( " \n" ); document.write( "

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